1. Field of Invention
The present invention is related to measuring magnetization of magnetic fluid. More particularly, the present invention relates to device for measuring ac magnetization of materials and method for detecting bio-molecules.
2. Description of Related Art
Magnetic fluid is a colloid solution having magnetic nanoparticles dispersed in solvent. The material of magnetic nanoparticles is usually ferromagnetic. Thus, each magnetic nanoparticle owns permanent magnetic moment. In order to disperse stably magnetic nanoparticles in solvent, magnetic nanoparticles are coated with surfactant. For example, hydrophilic organic material is used for surfactant to disperse magnetic nanoparticles into aqueous solution. With aid of surfactant and nano-scale size, magnetic nanoparticles can be dispersed individually in solvent. Due to thermal energy, individual magnetic nanoparticles experience Brownian motion. Although each magnetic nanoparticle is ferromagnetic, i.e. exhibiting permanent magnetic moment, the directions of magnetic moments of magnetic nanoparticles are isotropic in liquid under zero magnetic field, so that the resultant magnetic moment of magnetic nanoparticles in liquid is zero under zero magnetic field. However, as a magnetic field is applied to magnetic fluid, magnetic moment of each magnetic nanoparticle tends to be aligned with the direction of the applied magnetic field. The theoretical analysis for the resultant magnetic moment (hereafter referred as to magnetization) M of magnetic fluid under an applied magnetic field H at temperature T can be expressed as Langevin functionM(ξ)=Mo(cothξ−1/ξ).   (1)
In Eq. (1), Mo, in which Mo=Nm, N is the total numbers of magnetic nanoparticles and m is the averaged magnetic moment of a magnetic particle, denotes the saturated magnetization, and ξ can be written asξ=μomH/kBT,  (2)where H is the applied magnetic field, kB is Boltzmann constant, μ0 is permeability of free space, and T represents the measurement temperature.
According to Eq. (1) and Eq. (2), at a given temperature T, the magnetization M of magnetic fluid increases monotonously with the increasing strength H of magnetic field, and then reaches to a saturated value under high H's. This saturated magnetization is Mo in Eq. (1). When the applied magnetic field H is removed, i.e. H=0, the magnetization of magnetic fluid vanishes. The reversely zero magnetization of magnetic fluid as quenching an applied magnetic field is contributed by the directional randomization of magnetic moment of individual magnetic nanoparticles undergoing Brownian motion in liquid. This feature is so-called superparamagnetism.
In case of weak magnetic field being in several Gauss at room temperature (T about 300 K), ξ is around 10−3 to 10−2. Thus, the M in Eq. (1) can be expanded around ξ being zero via Taylor expansion and is written asM(ξ→0)=M(0)+M(1)(0)·ξ+M(2)(0)·ξ2+M(3)(0)·ξ3+M(4)(0)·ξ4+M(5)(0)·ξ5+ . . . ,   (3)where M(n) denotes the nth derivation of M with respect to ξ at ξ=0. One can find that the even-nth-derivation terms on the right-hand side of Eq. (3) become zero, and M(1)=0.32, M(3)=−0.12. Eq. (3) can be expressed asM(ξ→0)=0.32MoμomH/kBT−0.12Mo(μomH/kBT)3+O5(μomH/kBT)+ . . .   (4)
The fifth order of O5 on the right-hand side in Eq. (4) denotes the term of power 5 of μomH/kBT. If the applied magnetic field is generated by alternative-current (ac) and shows a frequency fo, it can be found that the M exhibits non-zero components at frequencies of αfo, where α is positive odd integers. Consequently, magnetic fluid shows magnetization having frequencies of not only fo but also αfo under a weak ac magnetic field with frequency fo.
In Eq. (1) or (4), Mo is proportional to the total numbers N of individual magnetic nanoparticles showing response to the applied ac magnetic field. Thus, in a given volume of magnetic fluid and under a fixed weak ac magnetic field having frequency fo, the amplitude of αfo-component of the magnetization M spectrum decreases when the total numbers N of individual magnetic nanoparticles is reduced. The reduction in the total numbers N of individual magnetic nanoparticles showing a response to the applied ac magnetic field can be achieved by making magnetic nanoparticles clustered or larger through certain reactions in liquid. For example, the certain reactions can be the association between bio-probes and bio-targets in liquid. In such case, bio-probes are coated onto individual magnetic nanoparticles via the binding to the surfactant. Thus, magnetic nanoparticles become bio-functional and are able to bind with conjugated bio-targets.
For instance, the antibody acts as bio-probes and is coated onto individual magnetic nanoparticles in liquid. These bio-functionalized magnetic nanoparticles can bind with conjugated antigens. Due to the association between antigens and antibodies on individual magnetic nanoparticles, magnetic nanoparticles become clustered or larger. Hence, the total number N of individual magnetic nanoparticles in response to an applied ac magnetic field at certain fixed frequency is definitely reduced. So, it can be deduced that the amplitude of αfo-component of the magnetization M of bio-functionalized magnetic fluid decreases when magnetic nanoparticles bind with bio-targets. Furthermore, the decreasing in the amplitude is enhanced when more individual magnetic nanoparticles bind with bio-targets. Hence, the amount of bio-targets can be determined by measuring the reduction in the αfo-component of the magnetization M of bio-functionalized magnetic fluid. This is the fundamental mechanism for such bio-assay technology as immunomagnetic reduction (IMR).
In order to measure the ac magnetization of the sample, several conventional apparatus have been proposed. FIG. 1 schematically shows the conventional architecture to measure the magnetization of magnetic fluid under an ac magnetic field. An excitation solenoid 102 is driven by an ac current generator 100 at frequency fo, so as to generate the ac magnetic field. A pick-up solenoid 104 is co-axially located inside the excitation solenoid 102. The pick-up solenoid 104 is referred as to magnetometer type. The magnetic fluid 108 is disposed inside the pick-up solenoid 104. The coil 106 is formed by the solenoids 102 and 104. The ac current generator 100 applies ac current at the frequency fo to the solenoid 102 of coil 106. Due to varying magnetic field, the pick-up solenoid 104 of coil 106 is induced ac voltage for output. However, the output of the ac voltage is relating to the magnetic fluid 108. As the ac magnetic field of frequency fo is applied, the magnetic fluid 108 is induced to generate ac magnetizations of various frequencies αfo, α=1, 3, 5, . . . n. The ac magnetizations are detected with the pick-up solenoid 104 of coil 106, which converts the signals from magnetization to voltage. Thus, ac voltages of frequencies αfo are output from the pick-up solenoid 104 of coil 106 to an electronic circuit 110. The electronic circuit 110 processes the voltage signals, with respect to various frequency components, to obtain the quantity at the component with the target frequency αTfo.
However, the measurement architecture shown in FIG. 1 has disadvantages. Firstly, in addition to the magnetizations generated by magnetic fluid, the ambient signals can be detected by the pick-up solenoid. Secondly, the ac magnetic field (at fo) generated with the excitation solenoid 102 is also probed. Thus, the induced voltage of fo at the output of the pick-up solenoid 104 is much stronger than those at other frequencies. For the electronic circuit 110, it usually has amplifying units to amplify the voltage signal at αTfo for achieving high detection sensitivity. The amplifying units are operation amplifiers, having high-level limitation for the input voltages. The operation amplifiers can not properly work when input voltage is too high. When the input voltage at αTfo is amplified, the input voltage at fo is also amplified. With the high-level limitation of operation amplifiers, there is a limitation to amplify the voltage signal at αTfo in order to keep the total input voltages below the high-level limitation of operation amplifiers. Thirdly, due to the sub-harmonic effect of electronic circuit, there exit output voltages at frequencies of fo, 2fo, 3fo, 4fo, 5fo, . . . etc., when there is input voltage at fo from the output of the pick-up solenoid 104. These negative factors cause that the resultant output voltage of αTfo from the electronic circuit is attributed to the ambient signals, the excitation field, and sub-harmonic signals of electronic circuit. Therefore, the final output voltage at αTfo is not reliable, or even false.
To overcome the disadvantages in FIG. 1, another conventional design to measure the induced ac magnetization of magnetic fluid is proposed. FIG. 2 schematically shows the conventional architecture to measure the magnetization of magnetic fluid under an ac magnetic field. In FIG. 2, the pick-up solenoid 120 includes two sections: upper section and lower section. The coils in these two sections are wired in opposite direction and connected in series. The magnetic fluid 108 is disposed at one of the two sections, such as the upper section. Thus, ambient signals can be simultaneously sensed by these two sections. Voltages can be induced from out-leads of these two sections, and are cancelled with each other. Besides, by well aligning the position of the pick-up solenoid 120 inside the excitation solenoid 102, the induced voltage at fo by the ac magnetic field at fo generated by the excitation solenoid 102 are cancelled for the gradiometer-type pick-up solenoid 120. In practical cases, it is impossible to completely cancel the induced voltage at fo by aligning the pick-up solenoid 120 inside the excitation solenoid 102. But, the input voltage at fo to the electronic circuit can be greatly reduced for the measurement architecture in FIG. 2 as compared to that in FIG. 1. This means that the amplification in the electronic circuit can be significantly increased when using gradiometer-type pick-up solenoid. However, the existence of input voltage of fo also generates the sub-harmonic signals to the output as mentioned before. Thus, the signals from the sample at the target frequency αTfo usually have unwanted components.
In conclusion, the conventional designs can measure the ac magnetization of magnetic fluid. However, the target frequency is limited to αTfo, multiple of base frequency fo, resulting in unreliable output voltage at αTfo and their applications are limited.